GridSurface Class

public abstract class GridSurface : Surface

Public MustInherit Class GridSurface
	Inherits Surface

public ref class GridSurface abstract : public Surface

[<AbstractClassAttribute>]
type GridSurface = 
    class
        inherit Surface
    end

Inheritance

Object  →  Surface  →  GridSurface

Derived

Numerics.NET.Curves.Surfaces.CubicGridSurface2D

Numerics.NET.Curves.Surfaces.CubicGridSurface3D

Numerics.NET.Curves.Surfaces.LinearGridSurface

Numerics.NET.Curves.Surfaces.NearestGridSurface

Numerics.NET.Curves.Surfaces.TensorSplineGridSurface

The GridSurface class performs interpolation on rectilinear grids where each axis has its own coordinate vector. Grid points are defined by the Cartesian product of these axis coordinates, and function values are stored in row-major order.

A rectilinear grid (also called a product grid) consists of independent coordinate vectors for each dimension. Unlike regular grids, rectilinear grids allow non-uniform spacing along each axis while maintaining axis-aligned structure.

Interpolation methods:

• Nearest-neighbor (CreateNearest): Returns the value at the closest grid point. Fast but discontinuous.
• Linear (multilinear) (CreateLinear): Performs bilinear (2D), trilinear (3D), or multilinear (N-D) interpolation within each grid cell. Continuous but with discontinuous first derivatives at cell boundaries.
• Cubic spline (CreateCubic): Uses specialized 2D/3D cubic surfaces based on CubicSpline with full CubicSplineKind options. Available only for 2D and 3D grids.
• Tensor-product splines (CreateCubicTensorSpline, CreateTensorSpline): Uses N-dimensional tensor-product interpolation with pluggable 1D spline kernels (ISplineKernel1D). Works for any dimension and supports custom kernels via SplineKernels.

Array dimension order: Values are stored in row-major (C-style) order where the last dimension varies fastest. For 2D grids: values[i, j] = f(xAxis[i], yAxis[j]). For 3D grids: values[i, j, k] = f(xAxis[i], yAxis[j], zAxis[k]).

Boundary conditions and extrapolation: The class distinguishes between construction-time GridBoundaryCondition (which affects how tensor-product splines handle out-of-range samples during stencil assembly) and evaluation-time ExtrapolationMode (which controls behavior for query points outside the grid domain). Each surface has a DefaultExtrapolationMode, and evaluation methods support per-call extrapolation mode overrides.

Creating instances: Do not instantiate concrete subclasses directly. Instead, use the static factory methods on GridSurface: CreateNearest(IReadOnlyList<IReadOnlyList<Double>>, IReadOnlyList<Double>, ExtrapolationMode), CreateLinear(IReadOnlyList<IReadOnlyList<Double>>, IReadOnlyList<Double>, ExtrapolationMode), CreateCubic(IReadOnlyList<IReadOnlyList<Double>>, IReadOnlyList<Double>, ExtrapolationMode), CreateCubicTensorSpline(IReadOnlyList<IReadOnlyList<Double>>, IReadOnlyList<Double>, GridBoundaryCondition, ExtrapolationMode), and CreateTensorSpline(IReadOnlyList<IReadOnlyList<Double>>, IReadOnlyList<Double>, ISplineKernel1D, GridBoundaryCondition, ExtrapolationMode).

Reference